Solve x^2+180x-36

$${ x }^{ 2 } +180x-36$$

Factor

$$\left(x-\left(-6\sqrt{226}-90\right)\right)\left(x-\left(6\sqrt{226}-90\right)\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$x^{2}+180x-36=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-180±\sqrt{180^{2}-4\left(-36\right)}}{2}$$

Square 180.

$$x=\frac{-180±\sqrt{32400-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$x=\frac{-180±\sqrt{32400+144}}{2}$$

Add 32400 to 144.

$$x=\frac{-180±\sqrt{32544}}{2}$$

Take the square root of 32544.

$$x=\frac{-180±12\sqrt{226}}{2}$$

Now solve the equation x=\frac{-180±12\sqrt{226}}{2} when ± is plus. Add -180 to 12\sqrt{226}.

$$x=\frac{12\sqrt{226}-180}{2}$$

Divide -180+12\sqrt{226} by 2.

$$x=6\sqrt{226}-90$$

Now solve the equation x=\frac{-180±12\sqrt{226}}{2} when ± is minus. Subtract 12\sqrt{226} from -180.

$$x=\frac{-12\sqrt{226}-180}{2}$$

Divide -180-12\sqrt{226} by 2.

$$x=-6\sqrt{226}-90$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -90+6\sqrt{226} for x_{1} and -90-6\sqrt{226} for x_{2}.

$$x^{2}+180x-36=\left(x-\left(6\sqrt{226}-90\right)\right)\left(x-\left(-6\sqrt{226}-90\right)\right)$$

Evaluate

$$x^{2}+180x-36$$